The present invention relates generally to the field of modems, and, more particularly, to the construction and optimization of signal constellations for data transmission based on available signal alphabets that are either known a priori, determined through identification of model parameters, or estimated during modem start-up by means of learning techniques.
Although the preferred embodiment will be described with respect to a pulse code modulation (PCM) modem, the present invention is in no way limited to PCM type modems and may be used with non-PCM modems. The present invention relates to the construction and optimization of signal constellations for the downlink of a PCM modem communication, system. The communications channel of interest for PCM modems is shown in FIG. 1. A digital modem 10 is connected to the digital transport 20, which is connected by means of a D/A converter 30 in a PCM codec 40 to the subscriber line 50. An analog modem 60 is connected to the opposite end of the subscriber line 50.
PCM modems such as modems according to ITU-T Recommendation V.90 employ pulse-amplitude modulation (PAM) for downstream signaling, where the signal constellations are sets of PCM codes according to the ITU-T Recommendation G.711 transmitted by the digital modem and corresponding voltage levels, at a given point of reference. Unless specified otherwise, the point of reference will be the output of the D/A converter 30 in the PCM codec 40, which is typically located at the Central Office.
For downstream data transmission according to Recommendation V.90, data bits are mapped to PCM codes according to Recommendation G.711 by the digital modem. The PCM codes are sent through the digital network and converted to analog voltage levels by the D/A converter in the PCM codec 40 of the Central Office. In mu-law networks, robbed-bit signaling (RBS) is often used for in-band call control, which results in the least-significant bit of a PCM code being unavailable for PCM modem data transmission. Moreover, digital attenuation pads with numerous attenuation levels and implementation characteristics are employed in the digital network. Both RBS and digital attenuation pads act as impairments from the perspective of PCM modem data transmission.
Due to the frame structure present on digital T1 links, a frame size of 6 modulation intervals T (6 samples at 8000 samples/second) was selected for downstream data transmission in V.90. Generally, the combination of impairments, such as RBS, digital pads, and PCM codec infidelity, may be different for each interval of a 6T frame. Since certain clusters of PCM codes are mapped by the digital impairments to the same PCM code, only a subset of non-overlapping PCM codes (with one representative from each cluster) can be used for data signaling in any of the 6 intervals, and the 6 subsets are generally different. Recomnnendation G.711 specifies the voltage levels at the D/A converter output corresponding to the 256 PCM codes. However, the subset of these PCM codes that is actually used is not known in advance. Moreover, the true voltage levels corresponding to these remaining PCM codes may differ significantly from the ideal levels specified by G.711 due to PCM codec infidelity and other impairments.
The presence of a priori unknown impairments in both the digital network and the PCM codec may require precise identification of the voltage levels corresponding to transmitted PCM codes, independently for each interval of a frame (cf. related U.S. application Ser. No. 09/264,272). The Recommendation V.90 uses a frame size of 6 modulation symbols, at a rate of 8000 symbols/second. In V.90 start-up, for example, this identification can be accomplished by the analog modem by using the DIL (Digital Impairment Learning) sequence of Phase 3 of the startup procedure. After an initial training of the analog modem""s equalizer (cf. related U.S. application Ser. No. 09/264,085), the voltage levels (i.e. signal levels) corresponding to transmitted PCM codes are learned separately for each interval in a frame of 6 modulation intervals.
The V.90 Recommendation allows up to 6 different signal constellations, which may be selected and assigned to intervals of a data frame by the analog modem. These constellations may be selected with a suitable spacing between adjacent signal levels to allow for reliable data transmission in the presence of noise and other distortions while maximizing the data rate subject to a constraint on average power. In practice, reliability is specified in terms of a desired probability of symbol error.
A significant constraint may be the power limit as well as the point of reference for measuring power imposed by country-specific regulations. The power limit and point of reference are sent by the digital modem to the analog modem during V.90 start-up. If the point of reference is at the output of the PCM codec and the presence of digital pads is detected, the analog modem can compensate for the attenuation and achieve higher data rates.
The problem of constellation generation in a V.90 modem is made significantly more difficult by the wide range of PCM-modem specific impairments under which near-optimal constellations must be selected. Another complication is that the impairments encountered for a particular connection may be unpredictable and may change from call to call. Furthermore, a V.90 modem may have only a limited amount of time available during start-up for selecting optimal signal constellations.
The problem of constellation generation for PCM modems was described in a TR-30.1 contribution by R. Fischer and G. Ungerboeck. However, no practical solution for solving the optimization problem with finite computational resources was proposed. Also, in U.S. Pat. No. 5,831,561 (hereinafter xe2x80x9cthe ""561 patentxe2x80x9d), the use of learned levels as the source of a signaling alphabet is described. However, little detail is provided as to how to build a constellation other than by selecting a larger number of available points and then reducing the number of points to the desired number of points by optimizing the minimum distance between points. Thus, the ""561 patent assumes a first data rate and then finds an achievable data rate based on the assumed data rate. The assumption of a first data rate is not necessary in the present invention.
Certain objects, advantages, and features of the invention will be set forth in the description that follows and will become apparent to those skilled in the art upon examination of the following or may be learned with the practice of the invention.
It is an object of the present invention to provide an improved method for the selection and optimization of a set of signal constellations for data transmission.
It is another object of the present invention that it can be used in a V.90 client or other PCM modem to select a set of signal constellations for downstream data transmission.
It is yet another object of the present invention to allow for the selection of near-optimal signal constellations as subsets of available signal alphabets. Specifically, for PCM modem channels, the available signal alphabets are dependent on the digital impairments encountered in a particular modem connection.
Another object of the present invention is to reduce or eliminate dependencies on a precise model of the impairments in the digital network and the PCM codec in constellation generation.
A further object of the present invention is to automatically take into account the effect of impairments for a wide range of PCM-modem specific impairments.
Another object of the present invention is to provide flexibility in selecting the signal constellations for different power limits and target error probabilities.
These and other objects of the present invention may be provided by methods, systems and computer program products for constellation generation which determine the range of available and usable ucodes and an initial minimum spacing between signal levels. A work constellation set is generated based on the initial range of ucodes and the initial minimum signal level spacing. The work constellation set is then iteratively adjusted so as to provide a work constellation set which achieves an error probability target. The work constellation set is then iteratively pruned so as to provide a pruned work constellation set which achieves a power limit. The pruned work constellation set is then iteratively fine-tuned so as to provide a final constellation set which is within a specified tolerance of the error probability target and/or the power limit.
In a further embodiment, the power limit may be enforced utilizing an exact distribution of the final constellation. Furthermore, the initial minimum signal level spacing may be determined based on mean squared error and a target symbol error probability.
In a particular embodiment of the present invention, the work constellation set is iteratively adjusted by reducing the minimum signal level spacing in order to approximate a target symbol error probability. Such an iterative reduction may be achieved by iteratively reducing the minimum signal level spacing until the symbol error probability of the work constellation set slightly exceeds a target symbol error probability. Furthermore, the minimum signal level spacing may finally be set to a value between a first minimum signal level spacing which results in a work constellation set with a symbol error probability below the target symbol error probability and the minimum signal level spacing which results in the symbol error probability of the work constellation set slightly exceeding the target symbol error probability.
In another embodiment of the present invention, the work constellation set is iteratively pruned by eliminating a largest signal level from the work constellation set. The iterative elimination of the largest signal level in the work constellation set is repeated until a constellation power below the power limit is reached.
In still another embodiment of the present invention, the work constellation set is iteratively fine-tuned by increasing the minimum signal level spacing until the constellation power of the resulting work constellation set is within a threshold value of the power limit. Furthermore, the multiplicity of signal levels which are at the minimum spacing with respect to a neighboring signal level, may also be reduced to fine-tune the work constellation set.
In preferred embodiments of the present invention, the work constellation sets at different stages of the described optimization have a signal-point distribution that is close to uniform, simplifying the computation of average power or symbol error probability.
In still another embodiment of the present invention, the initial minimum signal level spacing is established as a function of mean squared error.
In particular embodiments of the present invention, the minimum signal level spacing is reduced by determining       d          min      ,      LB        =            min              0        ≤        i        ≤        5              ⁢          min      ⁡              (                              2            ⁢                          c                              i                ,                0                            xe2x80x2                                ,                                    c                              i                ,                1                            xe2x80x2                        -                          c                              i                ,                0                                                    )            
where dmin,LB is the minimum signal level spacing and cxe2x80x2i0 and cxe2x80x2i1 are reduced smallest and second smallest signal levels and ci,0 is a previous smallest signal level of the work constellation set and wherein i is a frame interval. Furthermore, the largest level which is pruned may be the largest level satisfying (Mixe2x88x921)(Pxe2x88x92Q)xe2x89xa7Q, wherein Mi is a number of levels being used in a frame interval i, P is the product of all the Mi values and Q is 2K where K=└log2(P)┘.
If the attenuation due to digital pads in the network is known, the present invention may benefit from this knowledge by taking it into account in the computation of average power. Moreover, the present invention may provide fine control on how closely the power limit or error probability target are approximated. The present invention also is memory efficient as large tables of parameters corresponding to a wide range of impairments as well as input parameters are not required.
Preferably, the iterative operations are partitioned into submethods for flexibility and to allow a computationally efficient implementation. One submethod may allow an efficient selection of the minimal spacing between signal levels to approximate the target symbol error rate. Another submethod may be used for pruning the work constellations in order to meet the power constraint. Yet another submethod may be used for efficiently modifying the work constellations to approach the power limit more closely, e.g., by increasing the minimal spacing between signal levels, or by not selecting some of the signal levels that are at the minimal spacing.